Students run through central Bristol. Photograph: Sam Frost for the Guardian

We gather at Trafalgar Square at 12 and run. The protesters say they do not want to be kettled like last week in Whitehall. And so the students, a block of teenagers with a sound system that plays the Imperial March from Star Wars, run under Admiralty Arch and into the Mall, then past the Treasury and into Parliament Square.

Whenever we see a block of police in neon jackets we run, or are chased away, sometimes down boulevards that are closed and empty, and sometimes through traffic-choked alleys. Tourists take photos. The odd white van toots at this mass of running students. An old man shouts: "Go back to bed!"

I do not know who is leading us, but we don't stop running. The march is fracturing – people are going up different streets and getting lost. Texts come through from the front, giving information. There may be a demonstration at Topshop, or maybe at Liberal Democrat HQ on Cowley Street. But no – we just run down Piccadilly Circus and into Regent Street, then Oxford Street. "I don't feel like a protester," says a music student. "I feel like a tourist."The students dance across Aldwych, singing It Must Be Love, by Madness, before breaking again into a run down to the Embankment. It feels like kiss chase – or, when I see a policeman punch a boy out of the way, entirely without provocation, punch chase. "I'm going," says one girl. "I have a seminar."

Soon, we are back in Trafalgar Square. We have played protest Monopoly for two hours and now we have stopped. The banners – Don't Put the Kettle On, Mr Cameron and I Can't Believe It's Not Thatcher – are lowered, and the leaders climb on the plinth below Nelson's column and speak, asking the students to come back next week. If we have been running from – or to – a fight all day, we get it now. A group of boys charge a police line and fall over. A smoke bomb is thrown, then a can of beer. The police move forward to kettle the students. And above us, on the steps of the National Gallery, tourists look confused at this vision of Britain 2010, angry and fighting in the snow.